Extracting neuro-phenotypes from the brain at rest Ga¨ el Varoquaux
Probing variations of the mind Psychiatry is defined by symptoms Diagnostic and Statistical Manual of Mental Disorders No known physio-pathology; Autism = ? Asperger Need quantitative phenotypes of brain function G Varoquaux 2
Probing variations of the mind Psychiatry is defined by symptoms Diagnostic and Statistical Manual of Mental Disorders No known physio-pathology; Autism = ? Asperger Need quantitative phenotypes of brain function Population imaging with rest fMRI UK Biobank [Miller... 2016] Easy to set up reproducibly Suitable for diminished patients Connectivity captures traits G Varoquaux 2
Functional connectomes No salient features in rest fMRI G Varoquaux 3
Functional connectomes Define functional regions [Varoquaux and Craddock 2013] G Varoquaux 3
Functional connectomes Define functional regions Learn interactions [Varoquaux and Craddock 2013] G Varoquaux 3
Functional connectomes Define functional regions Learn interactions Detect differences [Varoquaux and Craddock 2013] G Varoquaux 3
Outline 1 Functional regions 2 The connectome matrix 3 Biomarkers of autism G Varoquaux 4
1 Functional regions Need functional regions for nodes ⇒ Spatial analysis G Varoquaux 5
1 Functional regions Available “on the market” anatomical atlases, functional atlases, region extraction methods G Varoquaux 5
1 Functional regions Atlases based on anatomy Clustering tools Linear decomposition G Varoquaux 5
1 Anatomical Anatomical atlases do not resolve functional structures AAL Harvard Oxford G Varoquaux 6
1 Clustering approaches Group together voxels with similar time courses ... ... ... ... ... G Varoquaux 7
1 Clustering approaches K-Means Fast No spatial constraint (smooth the data) Related to [Yeo... 2011] Normalized cuts [Craddock... 2012] Slow Spatial constraints Very geometrical Ward clustering Very fast (even with many clusters) Spatial constraints G Varoquaux 8
1 Clustering approaches [Thirion... 2014] K-Means Fast No spatial constraint (smooth the data) Related to [Yeo... 2011] Empirical choice Based on cluster stability and fit to data Normalized cuts Large number of clusters: Ward [Craddock... 2012] Slow Spatial constraints Small number of clusters: Kmeans Very geometrical [Thirion... 2014] Ward clustering Very fast (even with many clusters) Spatial constraints G Varoquaux 8
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Language G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Audio G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Visual G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Dorsal Att. G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Motor G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Salience G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Ventral Att. G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Parietal G Varoquaux 9
1 Mixture models: linear decompositions Working hypothesis / model : Observing linear mixtures of networks at rest Time courses Observe a mixture How to unmix networks? G Varoquaux 9
1 Spatial modes: ICA decomposition voxels voxels voxels time time time = E · S N Y + 25 Decomposing time series into: covarying spatial maps, S uncorrelated residuals, N p ICA: minimize mutual information across S [Kiviniemi 2003, Beckmann 2005, Varoquaux 2010] G Varoquaux 10
1 Spatial modes: ICA decomposition voxels voxels voxels time time time = E · S N Y + 25 Decomposing time series into: covarying spatial maps, S uncorrelated residuals, N p ICA: minimize mutual information across S [Kiviniemi 2003, Beckmann 2005, Varoquaux 2010] G Varoquaux 10
1 Spatial modes: ICA decomposition voxels voxels voxels time time time = E · S N Y + 25 Decomposing time series into: covarying spatial maps, S uncorrelated residuals, N Sparse decompositions: sparse penalty on maps [Kiviniemi 2003, Beckmann 2005, Varoquaux 2010] G Varoquaux 10
1 ICA versus sparse decompositions ICA 1. Select signal of interest 2. Select “maximaly independent” ICs Sparse decomposition 2 E , ˆ ˆ � � � � S = argmin � Y − E S 2 + λ � S � � � � � � � � � 1 � S , E Penalization: sparse maps Data fit Joint estimation of signal space + components G Varoquaux 11
1 From group to subject networks MSDL Multi-Subject Dictionary Learning � � � Y s − E s S sT � 2 Fro + µ � S s − S � 2 � argmin + λ Ω( S ) Fro E s , S s , S subjects Data fit Subject Penalization: variability inject structure [Varoquaux... 2011, Abraham... 2013] G Varoquaux 12
1 From group to subject networks MSDL Create a region-forming penalty: Original Clustering Total-variationg Multi-Subject Dictionary Learning � � � Y s − E s S sT � 2 Fro + µ � S s − S � 2 � argmin + λ Ω( S ) Fro E s , S s , S subjects Data fit Subject Penalization: variability inject structure [Varoquaux... 2011, Abraham... 2013] G Varoquaux 12
Visual and motor system White matter Functional network Vascular system Inner nuclei Downloadable from Parietal webpage http://team.inria.fr/parietal
Brain parcellations Group ICA MSDL Ward K-Means [Abraham... 2013]
Brain parcellations Group ICA MSDL Ward K-Means [Abraham... 2013]
Brain parcellations Group ICA MSDL Ward K-Means [Abraham... 2013]
Functional regions Craddock Smith 2009 Abraham 2013 Ward AAL ICAs 2011 Ncuts TV-MSDL Harvard- High model K-Means Varoquaux Yeo 2011 Oxford order ICA 2011 Smooth- MSDL G Varoquaux 15
Functional regions Craddock Smith 2009 Abraham 2013 Ward AAL ICAs 2011 Ncuts TV-MSDL Harvard- High model K-Means Varoquaux Yeo 2011 Oxford order ICA 2011 Smooth- MSDL G Varoquaux 15
2 The connectome matrix How to capture and represent interactions? G Varoquaux 16
2 Correlations: observations and indirect effects Observations Direct connections Correlation Partial correlation 1 1 2 2 0 0 3 3 4 4 Covariance: Inverse covariance: scaled by variance scaled by partial variance G Varoquaux 17
2 Correlations: observations and indirect effects Observations Direct connections Correlation Partial correlation G Varoquaux 17
2 Inverse covariance and graphical model Gaussian graphical models Zeros in inverse covariance give conditional independence x i , x j independent Σ − 1 i , j = 0 ⇔ conditionally on { x k , k � = i , j } Sparse inverse covariance Shrunk estimator Estimator imposes zeros Estimates closer to 0 [Smith... 2011, Varoquaux... [Varoquaux and Craddock 2010b] 2013] G Varoquaux 18
2 Differences in correlations across subjects 0 0 0 0 Correlation matrices 5 5 5 5 10 10 10 10 15 15 15 15 20 20 20 20 25 25 25 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 0 0 0 Partial correlation matrices 5 5 5 5 10 10 10 10 15 15 15 15 20 20 20 20 25 25 25 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 3 controls, 1 severe stroke patient Which is which? G Varoquaux 19
2 Differences in correlations across subjects 0 0 0 0 Correlation matrices 5 5 5 5 10 10 10 10 15 15 15 15 20 20 20 20 25 Control 25 Control 25 Control 25 Large lesion 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 0 0 0 Partial correlation matrices 5 5 5 5 10 10 10 10 15 15 15 15 20 20 20 20 25 Control 25 Control 25 Control 25 Large lesion 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Spread-out variability in correlation matrices Noise in partial-correlations Strong dependence between coefficients [Varoquaux... 2010a] G Varoquaux 19
2 A toy model of differences in connectivity Two processes with different partial correlations K 1 : K 1 − K 2 : Σ 1 : Σ 1 − Σ 2 : + jitter in observed covariance MSE( K 1 − K 2 ): MSE( Σ 1 − Σ 2 ): Non-local effects and non homogeneous noise G Varoquaux 20
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